What is the solution for y^{''}+36y=sin(5x) ?

The solution for y^{''}+36y=sin(5x) is y=c_{1}cos(6x)+c_{2}sin(6x)+1/11 sin(5x)

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y^{''}+36y=sin(5x)

y^{^{''}} + 36 y = sin (5 x)

y = c_{1} cos (6 x) + c_{2} sin (6 x) + \frac{1}{11} sin (5 x)

Solution steps

y^{''} (x) + 36 y = sin (5 x)

Solve linear ODE:

y = c_{1} cos (6 x) + c_{2} sin (6 x) + \frac{1}{11} sin (5 x)

y = c_{1} cos (6 x) + c_{2} sin (6 x) + \frac{1}{11} sin (5 x)

y^{^{''}} - 2 y^{^{'}} + y = x (e^{x}) + 4

D (x) = 120 x - 3580

2 y^{^{''}} - 2 y^{^{'}} - 4 y = - x^{2}

y^{^{''}} - y^{^{'}} + y = 3 sin (t) - 9 e^{2 t}

y^{^{''}} - 2 y + 37 y = e^{x} cos (6 x)

What is the solution for y^{''}+36y=sin(5x) ?
The solution for y^{''}+36y=sin(5x) is y=c_{1}cos(6x)+c_{2}sin(6x)+1/11 sin(5x)